The London Stock Exchange has accused Macquarie of trying to buy it "on the cheap" as it again rejected a £1.5 billion hostile bid from the Australian bank.

LSE, which had already branded the 580p a share offer "derisory", said the price "ignored the quality and strength" of the business.

The rejection came just hours after Macquarie posted full details of its bid to LSE shareholders, claiming the offer was "attractive, certain and deliverable in cash".

It was the latest twist in the year-long battle for control of LSE.

Macquarie, with UK investments ranging from BBC Broadcast, the M6 Toll Road and Birmingham Airport, tabled its £1.5 billion hostile bid in December after months of speculation that it was pursuing LSE.

Yesterday it posted the offer to shareholders and said: "The offer of 580p in cash per LSE share is the only offer available to LSE shareholders."

The 580p offer is well below last night's closing share price of 615p, but Macquarie has complained that the value of the exchange has been inflated by ongoing takeover speculation.

The Australians said the offer was at a 67 per cent premium on LSE's share price before the markets got wind that it was interested.

It also said it was a "competitive valuation" compared with other recent transactions in the exchange sector.

Macquarie gave LSE shareholders until 3pm on January 31 to accept the offer.

But LSE hit back and said: "Macquarie's offer ignores the quality and strength of the Exchange's business and its long-term growth prospects. It is a blatant attempt to acquire the Exchange on the cheap."